Economic Complexity Limits Accuracy of Price Probability Predictions by Gaussian Distributions

Victor Olkhov
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Abstract

The accuracy of predictions of price and return probabilities substantially determines the reliability of asset pricing and portfolio theories. We develop successive approximations that link up predictions of the market-based probabilities of price and return for the whole stock market with predictions of price and return probabilities for stocks of a particular company and show that economic complexity limits the accuracy of any forecasts. The economic origin of the restrictions lies in the fact that the predictions of the m-th statistical moments of price and return require descriptions of the economic variables composed by sums of the m-th powers of economic or market transactions during an averaging time interval. The attempts to predict the n-th statistical moments of price and return of stocks that are under the action of a single risk result in estimates of the n-dimensional risk rating vectors for economic agents. In turn, the risk rating vectors play the role of coordinates for the description of the evolution of economic variables. The lack of a model description of the economic variables composed by sums of the 2-d and higher powers of market transactions causes that, in the coming years, the accuracy of the forecasts will be limited at best by the first two statistical moments of price and return, which determine Gaussian distributions. One can ignore existing barriers and limits but cannot overcome or resolve them. That significantly reduces the reliability and veracity of modern asset pricing and portfolio theories. Our results could be essential and fruitful for the largest investors and banks, economic and financial authorities, and market participants.
经济复杂性限制了高斯分布预测价格概率的准确性
价格和回报概率预测的准确性在很大程度上决定了资产定价和投资组合理论的可靠性。我们开发了连续的近似,将整个股票市场的基于市场的价格和回报概率的预测与特定公司股票的价格和回报概率的预测联系起来,并表明经济复杂性限制了任何预测的准确性。这些限制的经济学根源在于,对价格和收益的第m个统计时刻的预测需要对经济变量的描述,这些变量由平均时间间隔内经济或市场交易的第m次幂的总和组成。试图预测在单一风险作用下股票价格和收益的统计时刻,结果是对经济主体的n维风险评级向量的估计。而风险评级向量则扮演了描述经济变量演化的坐标角色。由于缺乏对经济变量的模型描述,这些经济变量是由二维和更高的市场交易力量的总和构成的,因此,在未来几年,预测的准确性最多将受到价格和回报的前两个统计时刻的限制,而这两个统计时刻决定了高斯分布。人们可以忽略现有的障碍和限制,但无法克服或解决它们。这大大降低了现代资产定价和投资组合理论的可靠性和准确性。我们的研究结果对最大的投资者和银行、经济和金融当局以及市场参与者来说可能是必不可少和富有成效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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